Majorization preservation of Gaussian bosonic channels

Abstract

It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states. The proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces a mean photon number order, thereby connecting the concepts of energy and disorder of a quantum state. As an application, the consequences of majorization preservation are investigated in the context of the broadcast communication capacity of bosonic Gaussian channels. Most of our results being independent of the bosonic nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a general tool that could prove useful in quantum information theory and quantum thermodynamics.

6 pages

References in corpus (5)

• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Majorization criterion for distillability of a bipartite quantum state
• Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture
• Passive states optimize the output of bosonic Gaussian quantum channels
• Interconversion of pure Gaussian states using non-Gaussian operations

Cited by in corpus (6)

• Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
• Geometric inequalities from phase space translations
• Partial order on passive states and Hoffman majorization in quantum thermodynamics
• Continuous majorization in quantum phase space
• Fock majorization in bosonic quantum channels with a passive environment
• Majorization ladder in bosonic Gaussian channels